1. **Problem statement:** Rotate the triangle with vertices at $(-3,-5)$, $(-1,4)$, and $(3,4)$ by 90° anticlockwise about the point $(-1,1)$. 2. **Formula for rotation about a point:** To rotate a point $(x,y)$ about a point $(h,k)$ by 90° anticlockwise, use: $$x' = h - (y - k)$$ $$y' = k + (x - h)$$ 3. **Apply the formula to each vertex:** - For $(-3,-5)$: $$x' = -1 - (-5 - 1) = -1 - (-6) = -1 + 6 = 5$$ $$y' = 1 + (-3 + 1) = 1 + (-2) = -1$$ - For $(-1,4)$: $$x' = -1 - (4 - 1) = -1 - 3 = -4$$ $$y' = 1 + (-1 + 1) = 1 + 0 = 1$$ - For $(3,4)$: $$x' = -1 - (4 - 1) = -1 - 3 = -4$$ $$y' = 1 + (3 + 1) = 1 + 4 = 5$$ 4. **New vertices after rotation:** $(5,-1)$, $(-4,1)$, and $(-4,5)$. 5. **Explanation:** Each vertex was shifted relative to the rotation point, rotated 90° anticlockwise, then shifted back. **Final answer:** The image of the triangle after rotation has vertices at $\boxed{(5,-1), (-4,1), (-4,5)}$.